A=x2-3x-1

Solution for A=x2-3x-1 equation:

=A2-3A-1

We move all terms to the left:

-(A2-3A-1)=0

We add all the numbers together, and all the variables

-(+A^2-3A-1)=0

We get rid of parentheses

-A^2+3A+1=0

We add all the numbers together, and all the variables

-1A^2+3A+1=0

a = -1; b = 3; c = +1;
Δ = b2-4ac
Δ = 32-4·(-1)·1
Δ = 13
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{13}}{2*-1}=\frac{-3-\sqrt{13}}{-2}
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{13}}{2*-1}=\frac{-3+\sqrt{13}}{-2}
$